Stochastic Integration and Differential Equations
Subtitle: A New Approach
By: by Philip Protter
Series: Applications of Mathematics -- 21; Applications of Mathematics -- 21
Publisher: Springer Berlin Heidelberg
Published: 1990
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 302
ISBN-13: 9783662026212; 9783662026199
Subjects: Mathematics; Distribution (Probability theory); Global analysis (Mathematics); Engineering mathematics
Description: This book is quite different from others on the subject in that it presents a rapid introduction to the modern semimartingale theory of stochastic integration and differential equations, without first having to treat the beautiful but highly technical "general theory of processes". The author's new approach (based on the theorem of Bitcheler-Dellacherie) also give a more intuitive understanding of the subject, and permits proofs to be much less technical. All of the major theorems of stochastic integration are given, including a comprehensive treatment (first time in English) of local times. A theory of stochastic differential equations driven by semimartingales is developed, including Fisk-Stratonovich equations, Markov properties, stability, and an introduction to the theory of flows. Further topics presented for the 1st time in book form include an elementary presentation of Azema's martingale. This book will quickly become a standard reference on the subject, to be used by specialists and non-specialists alike, both for the sake of the theory and for its application.
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